Question: Simplify; express your answer in exponential form. Assume $a\neq 0, k\neq 0$. $\dfrac{{(a^{5})^{3}}}{{a^{4}k^{4}}}$
To start, try working on the numerator and the denominator independently. In the numerator, we have ${a^{5}}$ to the exponent ${3}$ . Now ${5 \times 3 = 15}$ , so ${(a^{5})^{3} = a^{15}}$ In the denominator, we can use the distributive property of exponents. ${a^{4}k^{4} = a^{4}k^{4}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(a^{5})^{3}}}{{a^{4}k^{4}}} = \dfrac{{a^{15}}}{{a^{4}k^{4}}}$ Break up the equation by variable and simplify. $\dfrac{{a^{15}}}{{a^{4}k^{4}}} = \dfrac{{a^{15}}}{{a^{4}}} \cdot \dfrac{{1}}{{k^{4}}} = a^{{15} - {4}} \cdot k^{- {4}} = a^{11}k^{-4}$.